We report the observation of anomalous Hall resistivity in single crystals of ${\mathrm{EuAl}}_4$, a centrosymmetric tetragonal compound, which exhibits coexisting antiferromagnetic (AFM) and charge-density-wave (CDW) orders with onset at $T_{\mathrm{N}}\sim 15.6\mathrm{K}$ and $T_{\mathrm{CDW}}\sim 140\mathrm{K}$, respectively. In the AFM state, when the magnetic field is applied along the $c$-axis direction, ${\mathrm{EuAl}}_4$ undergoes a series of metamagnetic transitions. Within this field range, we observe a clear humplike anomaly in the Hall resistivity, representing part of the anomalous Hall resistivity. By considering different scenarios, we conclude that such a humplike feature is most likely a manifestation of the topological Hall effect, normally occurring in noncentrosymmetric materials known to host nontrivial topological spin textures. In view of this, ${\mathrm{EuAl}}_4$ would represent a rare case where the topological Hall effect not only arises in a centrosymmetric structure, but it also coexists with CDW order.

To trace the origin of time-reversal symmetry breaking (TRSB) in Re-based superconductors, we performed comparative muon-spin rotation and relaxation ($\mu \mathrm{SR}$) studies of superconducting noncentrosymmetric ${\mathrm{Re}}_{0.82}{\mathrm{Nb}}_{0.18}$ ($T_c=8.8\mathrm{K}$) and centrosymmetric Re ($T_c=2.7\mathrm{K}$). In ${\mathrm{Re}}_{0.82}{\mathrm{Nb}}_{0.18}$, the low–temperature superfluid density and the electronic specific heat evidence a fully gapped superconducting state, whose enhanced gap magnitude and specific-heat discontinuity suggest a moderately strong electron-phonon coupling. In both ${\mathrm{Re}}_{0.82}{\mathrm{Nb}}_{0.18}$ and pure Re, the spontaneous magnetic fields revealed by zero-field $\mu \mathrm{SR}$ below $T_c$ indicate time-reversal symmetry breaking and thus unconventional superconductivity. The concomitant occurrence of TRSB in centrosymmetric Re and noncentrosymmetric $\mathrm{Re}T$ ($T=\text{transition}$ metal), yet its preservation in the isostructural noncentrosymmetric superconductors ${\mathrm{Mg}}_{10}{\mathrm{Ir}}_{19}{\mathrm{B}}_{16}$ and ${\mathrm{Nb}}_{0.5}{\mathrm{Os}}_{0.5}$, strongly suggests that the local electronic structure of Re is crucial for understanding the TRSB superconducting state in Re and $\mathrm{Re}T$. We discuss the superconducting order parameter symmetries that are compatible with the experimental observations.

The noncentrosymmetric superconductor ${\mathrm{Re}}_{24}{\mathrm{Ti}}_5$, a time-reversal symmetry- (TRS-) breaking candidate with $T_c=6\mathrm{K}$, was studied by means of muon-spin rotation/relaxation ($\mu \mathrm{SR}$) and tunnel-diode oscillator techniques. At the macroscopic level, its bulk superconductivity was investigated via electrical resistivity, magnetic susceptibility, and heat-capacity measurements. The low-temperature penetration depth, superfluid density, and electronic heat capacity all evidence an $s$-wave coupling with an enhanced superconducting gap. The spontaneous magnetic fields revealed by zero-field $\mu \mathrm{SR}$ below $T_c$ indicate a time-reversal symmetry breaking and thus the unconventional nature of superconductivity in ${\mathrm{Re}}_{24}{\mathrm{Ti}}_5$. The concomitant occurrence of TRS breaking also in the isostructural ${\mathrm{Re}}_6(\mathrm{Zr},\mathrm{Hf})$ compounds hints at its common origin in this superconducting family and that an enhanced spin-orbital coupling does not affect pairing symmetry.

By employing a series of experimental techniques, we provide clear evidence that CaPtAs represents a rare example of a noncentrosymmetric superconductor which simultaneously exhibits nodes in the superconducting gap and broken time-reversal symmetry (TRS) in its superconducting state (below $T_c\approx 1.5\mathrm{K}$). Unlike in fully gapped superconductors, the magnetic penetration depth $\lambda (T)$ does not saturate at low temperatures, but instead it shows a $T^2$ dependence, characteristic of gap nodes. Both the superfluid density and the electronic specific heat are best described by a two-gap model comprising of a nodeless gap and a gap with nodes, rather than by single-band models. At the same time, zero-field muon-spin relaxation spectra exhibit increased relaxation rates below the onset of superconductivity, implying that TRS is broken in the superconducting state of CaPtAs, hence indicating its unconventional nature. Our observations suggest CaPtAs to be a new remarkable material that links two apparently disparate classes, that of TRS-breaking correlated magnetic superconductors with nodal gaps and the weakly correlated noncentrosymmetric superconductors with broken TRS, normally exhibiting only a fully gapped behavior.